I went back to “Paris Frocks At Home” and there it was! The illustrated instructions for finishing a neckline and armhole with binding make clear what has to be done.
Illustration from “Paris Frocks At Home”, published by Butterick Patterns, 1930. Page 80.
The instructions state that the seam allowance has to be cut away. The double bias binding is placed on the front of the bodice with the raw edge to the neckline. It is then stitched 1/8″ away . After this the binding is rolled to the inside and fell stitched in place.
What I did was get mixed-up after a busy day at work and rushing to sew the neckline after dinner. I cut away the neckline seam allowance but sewed so that it rested above the neckline, similar to the way a ribbed trim on a knit top is sewn in. When I try again I think this will work because the binding will be stabilized and held in place by the bodice fabric.
If you notice there is no mention of stay stitching along the neckline or armhole. This calls for a departure from remaining true to period techniques. I will definitely stay stitch my v-neckline. I might use a 1/8″ cotton stay tape or organza selvedge to further stabilize the neckline when I stay stitch.